Simplify the following expression: $ x = \dfrac{8z + 9}{5z} + \dfrac{4}{3} $
Solution: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{3}{3}$ $ \dfrac{8z + 9}{5z} \times \dfrac{3}{3} = \dfrac{24z + 27}{15z} $ Multiply the second expression by $\dfrac{5z}{5z}$ $ \dfrac{4}{3} \times \dfrac{5z}{5z} = \dfrac{20z}{15z} $ Therefore $ x = \dfrac{24z + 27}{15z} + \dfrac{20z}{15z} $ Now the expressions have the same denominator we can simply add the numerators: $x = \dfrac{24z + 27 + 20z}{15z} $ $x = \dfrac{44z + 27}{15z}$